A proper tensorial logarithmic strain measure and its associated time rate of change is developed using an equivalence between the expressions for an isotropic tensor function and the Sylvester‐Lagrange formalism. It is shown that the specific Cauchy stressT/&rgr; is derivable from a potential with respect to this strain measure. A modified stressTFis shown to be derivable from a potential with respect to the left polar decomposition of the deformation gradient. Advantages and disadvantages of this formulation are discussed.